Field of the Invention
The present invention relates to cup-type strain wave gearings, and in particular, relates to a small-size, cup-shaped flexible externally toothed gear for a cup-type strain wave gearing.
Description of the Related Art
FIG. 1A is a longitudinal cross sectional view showing a typical cup-type strain wave gearing, and FIG. 1B is a schematic diagram thereof when cut along a plane perpendicular to a center axis line of the device. As shown in these drawings, the strain wave gearing 1 has an annular rigid internally toothed gear 2, a cup-shaped flexible externally toothed gear 3 arranged inside the rigid internally toothed gear in a concentric manner, and an ellipsoidal-contoured wave generator 4 fitted inside the flexible externally toothed gear 3. The flexible externally toothed gear 3 has a flexible cylindrical body 11, a diaphragm 12 extending radially inward from one end of the cylindrical body in the direction of the center axis line 1a, and a rigid boss 13 continued to the inner peripheral edge of the diaphragm 12.
A portion of the cylindrical body 11 of the flexible externally toothed gear 3 where external teeth 14 are formed is flexed by the wave generator 4 into an ellipsoidal shape, whereby the external teeth 14 located on both ends in the major-axis direction of the ellipsoidal shape are meshed with internal teeth 15 of the rigid internally toothed gear 2. Since the difference in number of teeth between the both gears 2 and 3 is 2n (n is a positive integer), the meshing positions between the both gears 2 and 3 move circumferentially to generate relative rotation between the gears according to the difference in number of teeth when the wave generator 4 is rotated by a motor or another rotational source. Typically, the rigid internally toothed gear 2 is fixed so as not to rotate, and a greatly reduced-speed rotation is output from the flexible externally toothed gear 3.
FIGS. 2A, 2B and 2C are explanatory views showing longitudinal cross sections of the cup-shaped flexible externally toothed gear 3 before and after it is deformed. The cylindrical body 11 of the flexible externally toothed gear 3 has an original cylindrical shape before it is deformed as shown in FIG. 2A. After being deformed into an ellipsoidal shape by the wave generator 4, the cylindrical body 11 becomes a state in which the longitudinal cross sectional shape thereof including the major axis of the ellipsoidal shape is tapered outward from the side of the diaphragm 12 toward the open end 11a, as shown in FIG. 2B. Whereas, the longitudinal cross sectional shape of the cylindrical body 11 including the minor axis of the ellipsoidal shape is tapered inward from the side of the diaphragm 12 toward the open end 11a, as shown in FIG. 2C.
The diaphragm 12 is formed between the cylindrical body 11 and the rigid boss 13 in order for the portion of the cylindrical body 11 on the open end 11a side to be capable of being deformed into an ellipsoidal shape. When the portion including the open end 11a of the cylindrical body 11 is deformed into an ellipsoidal shape, the diaphragm 12 is bent backwards as shown by an arrow in FIG. 2B at a joint portion thereof joining to the rigid boss 13 in the longitudinal cross section including the major axis of the ellipsoidal shape. Whereas, the diaphragm 12 is bent forward toward the side of the open end 11a as shown by the arrow in FIG. 2C in the longitudinal cross section including the minor axis of the ellipsoidal shape. Thus, during the operation of the gearing 1, the diaphragm 12 is applied with bending stress in the direction of the center axis line 11b and, at the same time, is applied with share stress caused by torque transmission.
Taking into consideration of these stresses applied in combination to the diaphragm 12, the longitudinal cross sectional shape of the diaphragm 12 is designed so that the open-end side portion of the cylindrical body 11 is capable of being deformed into an ellipsoidal shape with a smaller force and that the diaphragm 12 is capable of transferring a larger torque. In particular, the longitudinal cross sectional shape of the diaphragm is designed so as to avoid stress concentration on the diaphragm in a state in which the combined stresses are applied.
Patent document 1 (Japanese Unexamined Utility Model Application Publication No. 61-173851) discloses a cup-shaped flexible externally toothed gear, in which the longitudinal cross sectional shape of a diaphragm is designed so that the inside end face thereof is defined by a straight line, and the outside end face thereof in the joint portion to the boss is defined by a streamline so as to gradually increase the thickness of the diaphragm.
Patent document 2 (WO 2013/024511) discloses a flexible externally toothed gear, in which the diaphragm as a whole is made slightly inclined with respect to a direction perpendicular to the center axis line, and the outside profile of the joint portion to the boss in the diaphragm is defined by three circular arcs.
The streamline, which is superior in dynamic characteristics, is employed to define the profile of the boss-side joint portion in the diaphragm of the cup-shaped flexible externally toothed gear. The streamline profile is constituted by three or more circular curves having different radii as disclosed in Patent Document 1. The circular curves are arranged so that the radii thereof become smaller toward the boss side.
The flexible externally toothed gear is usually manufactured by lathe turning. When small-size flexible externally toothed gears are concerned, the radii of the curves for constituting the streamline become smaller inevitably. It is therefore difficult to generate a profile shape of the boss-side joint portion in the diaphragm according to the streamline by making use of lathe turning.
Specifically, in commercially available typical lathe turning machines, the minimum value of the nose tip radius is 0.2 mm or larger. It is difficult to generate a profile shape of the boss-side joint portion of the diaphragm in case in which a streamline defined by circular curves including one having a radius smaller than 0.2 mm is employed. For example, when the flexible externally toothed gear is small in size and has a pitch circle diameter of 20 to 40 mm, if the profile shape of the boss-side joint portion in the diaphragm is defined by a streamline, curves that constitute the streamline include curves having a radius smaller than the minimum value of the nose tip radius of lathe turning machines.
Here, as shown in FIG. 3, it is considered to define the profile shape of the outside end face of the boss-side joint portion 42a in the diaphragm 42 by a circular arc 54 in place of the stream line, the circular arc 54 having a radius R3 that is the same as the minimum nose tip radius and is able to be processed by a commercially available lathe turning machine.
However, in the diaphragm 42 having the profile shape defined by the circular arc, the boss-side joint portion 42a may suffer from stress concentration that is greater than when the streamline profile is employed. This causes to decrease fatigue strength of the flexible externally toothed gear 40, and load capacity of the strain wave gearing cannot be enhanced.